Question

Prices register an increase of 10% on food grains and 15% on other items of expenditure. If the ratio of an employee expenditure on food grains and other items be 2:5, by how much should his salary be increased in order that he may maintain the same level of consumption as before his present salary being Rs. 2590.
A. Rs. 323.75
B. Rs. 350
C. Rs. 360.50
D. Rs. 351.50

Answer 1

Hint: To do this question, we will first calculate what amount of the salary is spent on food and on other items. Then, as we have been given that the employee’s consumption should remain the same, we will see that the percentage rise on food and other items should be equal to the percentage rise on the part of his salary on food and other items respectively. Thus, the total rise in his salary should be equal to 10% of what he spends on food currently plus 15% of what he spends on other items currently. Doing this, we will get our answer.

Complete step by step answer:
We here have been told that there is a 10% rise in the prices of food grains and 15% on that of other items of expenditure. We also have been told that the ratio of expenditure of an employee on food to that on other items is 2:5 and his salary is Rs. 2590.
Thus, we can calculate the amount of money he spends on each of them.
Hence, money spends on food grains will be given as:
\[\begin{align}
  & \dfrac{2}{2+5}\times 2950 \\
 & \Rightarrow \dfrac{2}{7}\times 2950 \\
 & \Rightarrow 2\times 370 \\
 & \Rightarrow Rs.740 \\
\end{align}\]
Thus, he spends Rs. 740 on his food grains every month,
Now, the money he spends on other items is given as:
$\begin{align}
  & \dfrac{5}{2+5}\times 2950 \\
 & \Rightarrow \dfrac{5}{7}\times 2950 \\
 & \Rightarrow 5\times 370 \\
 & \Rightarrow Rs.1850 \\
\end{align}$
Thus, he spends Rs. 1850 on other items than food every month.
Now, we have been told that the registered prices have been increased but the level of consumption should stay the same for this employee and hence we need to increase his salary in such a way that it does stay the same.
For this, the percentage increase in the prices should be equal to the percentage increase in his salary.
Thus, 10% of the part of his salary which he spends on food should be increased and 16=5% of that he spends on other items should increase.
Thus, the amount of the food part of the salary that should increase is given as:
10% of money spent on food presently
$\begin{align}
  & \Rightarrow \dfrac{10}{100}\times 740 \\
 & \Rightarrow Rs.74 \\
\end{align}$
Hence, Rs. 74 should increase on what he spends on his food presently.
Now, the amount of the other expenditure part of the salary that should increase is given as:
15% of money he spends on other items
$\begin{align}
  & \Rightarrow \dfrac{15}{100}\times 1850 \\
 & \Rightarrow Rs.277.50 \\
\end{align}$
Hence, Rs. 277.50 should increase on what he spends on his other expenditure items presently.
Hence, the total amount of increase on his salary is given as:
$\begin{align}
  & 74+277.50 \\
 & \therefore Rs.351.50 \\
\end{align}$
Hence, the required increase on salary is Rs. 351.50

So, the correct answer is “Option D”.

Note: We can also find the part of his salary that the man spent on by the following method:
The ratio given to us is 2:5. Now, let us assume that the factor here is x.
Thus, the part of his salary spent on food=2x
The part of salary spent on other items=5x
Now, we know that the total salary is equal to Rs. 2590.
Thus, we can say that:
$\begin{align}
  & 2x+5x=2590 \\
 & \Rightarrow 7x=2590 \\
 & \Rightarrow x=\dfrac{2590}{7}=370 \\
\end{align}$
Hence, the salary spent on food=$2x=2\left( 370 \right)=Rs.740$
Salary spent on other items= $5x=5\left( 370 \right)=Rs.1850$